Lie point symmetries and some group invariant solutions of the quasilinear equation involving the infinity Laplacian

Using the classical Lie method we obtain the full Lie point symmetry group of the Aronsson equation in two independent variables. Some group invariant solutions of this equation are found and a conjecture on the Lie point symmetry group of the Aronsson equation in Rⁿ is presented.     

On the local asymptotics of Faber polynomials

We study a local asymptotics of the (generalized) Faber polynomials at the boundary of the associated domain, under certain mild smoothness conditions on the weight function and geometric conditions on the boundary. The main result exhibits how this asymptotics depends on the corners at the boundary. Its proof is based on the continuity properties of the Visser-Ostrowski quotient at the corners.

     

A class of dimension-skipping graphs

Forn≧6 there exists a graphG with dimG=n, dimG*≧n+2, whereG* isG with a certain edge added.     

Geometry of rank 2 distributions with nonzero Wilczynski invariants

In the famous 1910 “cinq variables” paper Cartan showed in particular that for maximally nonholonomic rank 2 distributions in ?⁵ with non-zero covariant binary biquadratic form the dimension of the pseudo-group of local symmetries does not exceed 7 and among such distributions he described the one-parametric family of distributions for which this pseudo-group is exactly 7-dimensional. Using the novel interpretation of the Cartan covariant binary biquadratic form via the classical Wilczynski invariant of curves in projective spaces associated with abnormal extremals of the distributions [4, 27, 28] one can generalize this Cartan result to rank 2 distributions in ?ⁿ satisfying certain genericity assumption, called maximality of class, for arbitrary n ≥ 5.

In the present paper for any rank 2 distribution of maximal class with at least one nonvanishing generalized Wilczynski invariants we construct the canonical frame on a (2n — 3)-dimensional bundle and describe explicitly the moduli spaces of the most symmetric models. The relation of our results to the divergence equivalence of Lagrangians of higher order is given as well.     

High-frequency 263 GHz PELDOR

Pulsed electron–electron double resonance (PELDOR/DEER) at high frequencies can provide information on the relative orientation of paramagnetic centres or spin labels, if those are rigidly oriented in a host biomolecule and experiments are performed with sufficient orientation selectivity. We present the first comparative PELDOR study at 263 and 94 GHz on a model RNA system containing rigid nitroxides. We show that at 263 GHz still considerable modulation depth is observed and orientation selectivity is significant, particularly in g _x–g _y plane of the nitroxides.     

Evaluation of Activation Energies for Pairwise and Non-Pairwise Hydrogen Addition to Propyne Over Pd/Aluminosilicate Fiberglass Catalyst by Parahydrogen-Induced Polarization (PHIP)

Hydrogenation of propyne to propene over Pd/aluminosilicate fiberglass catalyst in the temperature range 175–350 °C was investigated with the use of parahydrogen-induced polarization (PHIP) technique. Activation energies for both pairwise and non-pairwise H₂ addition routes were estimated. It was found that at 175–275 °C the activation energies for hydrogen addition to the triple bond of propyne have similar values (about 60–70 kJ/mol) for both routes of hydrogen addition. At higher temperatures (275–350 °C), the rate constant for pairwise hydrogen addition reaches a maximum value while the rate constant for non-pairwise hydrogen addition continues to increase with increasing temperature.     

Quasifractional Approximants in the Theory of Composite Materials

We study the effective heat conductivity of regular arrays of perfectly conducting spheres embedded in a matrix with unit conductivity. Quasifractional approximants allow us to derive an approximate analytical solution, valid for all values of the spheres volume fraction [0, _max] (_max is the maximum volume fraction of a spheres). As a starting point we use a perturbation approach for 0 and an asymptotic solution for _max. Three different spatial arrangements of the spheres, simple cubic, body centred and face centred cubic arrays, are considered. Results obtained give a good agreement with numerical data.     

Magnetocaloric effect and multifunctional properties of Ni–Mn-based Heusler alloys

The studies of magnetocaloric properties, phase transitions, and phenomena related to magnetic heterogeneity in the vicinity of the martensitic transition (MT) in Ni–Mn–In and Ni–Mn–Ga off-stoichiometric Heusler alloys are summarized. The crystal structure, magnetocaloric effect (MCE), and magnetotransport properties were studied for the following alloys: Ni₅₀Mn_50−xIn_x, Ni_50−xCo_xMn₃₅In₁₅, Ni₅₀Mn_35−xCo_xIn₁₅, Ni₅₀Mn₃₅In₁₄Z (Z=Al, Ge), Ni₅₀Mn₃₅In_15−xSi_x, Ni_50−xCo_xMn_25+yGa_25−y, and Ni_50–xCo_xMn_32−yFeyGa₁₈. It was found that the magnetic entropy change, ΔS, associated with the inverse MCE in the vicinity of the temperature of the magneto-structural transition, TM, persists in a range of (125-5) J/(kg K) for a magnetic field change ΔH=5 T. The corresponding temperature varies with composition from 143 to 400 K. The MT in Ni₅₀Mn_50−xIn_x (x=13.5) results in a transition between two paramagnetic states. Associated with the paramagnetic austenite-paramagnetic martensite transition ΔS=24 J/(kg K) was detected for ΔH=5 T at T=350 K. The variation in composition of Ni₂MnGa can drastically change the magnetic state of the martensitic phase below and in the vicinity of TM. The presence of the martensitic phase with magnetic moment much smaller than that in the austenitic phase above TM leads to the large inverse MCE in the Ni₄₂Co₈Mn_32−yFeyGa₁₈ system. The adiabatic change of temperature (ΔT_ad) in the vicinity of TC and TM of Ni₅₀Mn₃₅In₁₅ and Ni₅₀Mn₃₅In₁₄Z (Z=Al, Ge) was found to be ΔT_ad=−2 K and 2 K for ΔH=1.8 T, respectively. It was observed that |ΔT_ad|≈1 K for ΔH=1 T for both types of transitions. The results on resistivity, magnetoresistance, Hall resistivity in some In-based alloys are discussed.     

Removability of isolated singularity for anisotropic parabolic equations with absorption

We study the problem of removability of isolated singularity for general quasilinear anisotropic parabolic equations with absorption. The precise conditions on the behaviour of the absorption term that ensure the non-existence of solutions with point singularities are established.